A symmetric low-regularity integrator for nonlinear Klein-Gordon equation

In this work, we propose a symmetric exponential-type low- regularity integrator for solving the nonlinear Klein-Gordon equation under rough data. The scheme is explicit in the physical space, and it is efficient under the Fourier pseudospectral discretization. Moreover, it achieves the second-order accuracy in time without loss of regularity of the solution, and its time-reversal symmetry ensures the good long-time behavior. Error estimates are done for both semi- and full discretizations. Numerical results confirm the theoretical results, and comparisons illustrate the improvement of the proposed scheme over the existing methods.